Bilinear estimates and applications to nonlinear wave equations

Sergiu Klainerman, Sigmund Selberg

Research output: Contribution to journalArticlepeer-review

67 Scopus citations

Abstract

We undertake a systematic review of results proved in [26, 27, 30-32] concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we give a considerably simplified and unified treatment of these results and provide also complete proofs for large data. The paper is also intended as an introduction to and survey of current research in the very active area of nonlinear wave equations. The key ingredients throughout the survey are the use of the null structure of the equations we consider and, intimately tied to it, bilinear estimates.

Original languageEnglish (US)
Pages (from-to)223-295
Number of pages73
JournalCommunications in Contemporary Mathematics
Volume4
Issue number2
DOIs
StatePublished - Aug 19 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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